diff --git a/Tests/images/drawing_roundDown.emf b/Tests/images/drawing_roundDown.emf
new file mode 100644
index 000000000..6c3e20248
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diff --git a/Tests/images/hopper_roundDown.bmp b/Tests/images/hopper_roundDown.bmp
new file mode 100644
index 000000000..62aada050
Binary files /dev/null and b/Tests/images/hopper_roundDown.bmp differ
diff --git a/Tests/images/hopper_roundDown_2.tif b/Tests/images/hopper_roundDown_2.tif
new file mode 100644
index 000000000..ac8cd057d
Binary files /dev/null and b/Tests/images/hopper_roundDown_2.tif differ
diff --git a/Tests/images/hopper_roundDown_3.tif b/Tests/images/hopper_roundDown_3.tif
new file mode 100644
index 000000000..0542fab9a
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diff --git a/Tests/images/hopper_roundDown_None.tif b/Tests/images/hopper_roundDown_None.tif
new file mode 100644
index 000000000..21c40e8fe
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diff --git a/Tests/images/hopper_roundUp_2.tif b/Tests/images/hopper_roundUp_2.tif
new file mode 100644
index 000000000..e38541c5d
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diff --git a/Tests/images/hopper_roundUp_3.tif b/Tests/images/hopper_roundUp_3.tif
new file mode 100644
index 000000000..af6c96bd4
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diff --git a/Tests/images/hopper_roundUp_None.tif b/Tests/images/hopper_roundUp_None.tif
new file mode 100644
index 000000000..b98635108
Binary files /dev/null and b/Tests/images/hopper_roundUp_None.tif differ
diff --git a/Tests/images/iptc_roundDown.jpg b/Tests/images/iptc_roundDown.jpg
new file mode 100644
index 000000000..f98206f18
Binary files /dev/null and b/Tests/images/iptc_roundDown.jpg differ
diff --git a/Tests/images/iptc_roundUp.jpg b/Tests/images/iptc_roundUp.jpg
new file mode 100644
index 000000000..68ac20b71
Binary files /dev/null and b/Tests/images/iptc_roundUp.jpg differ
diff --git a/Tests/test_file_bmp.py b/Tests/test_file_bmp.py
index ec651ae8c..b97a84227 100644
--- a/Tests/test_file_bmp.py
+++ b/Tests/test_file_bmp.py
@@ -71,6 +71,27 @@ class TestFileBmp(PillowTestCase):
         self.assertEqual(im.size, reloaded.size)
         self.assertEqual(reloaded.format, "JPEG")
 
+    def test_load_dpi_rounding(self):
+        # Round up
+        im = Image.open('Tests/images/hopper.bmp')
+        self.assertEqual(im.info["dpi"], (96, 96))
+
+        # Round down
+        im = Image.open('Tests/images/hopper_roundDown.bmp')
+        self.assertEqual(im.info["dpi"], (72, 72))
+
+    def test_save_dpi_rounding(self):
+        outfile = self.tempfile("temp.bmp")
+        im = Image.open('Tests/images/hopper.bmp')
+
+        im.save(outfile, dpi=(72.2, 72.2))
+        reloaded = Image.open(outfile)
+        self.assertEqual(reloaded.info["dpi"], (72, 72))
+
+        im.save(outfile, dpi=(72.8, 72.8))
+        reloaded = Image.open(outfile)
+        self.assertEqual(reloaded.info["dpi"], (73, 73))
+
     def test_load_dib(self):
         # test for #1293, Imagegrab returning Unsupported Bitfields Format
         im = Image.open('Tests/images/clipboard.dib')
diff --git a/Tests/test_file_jpeg.py b/Tests/test_file_jpeg.py
index 712a36cd5..25c3f754a 100644
--- a/Tests/test_file_jpeg.py
+++ b/Tests/test_file_jpeg.py
@@ -524,6 +524,27 @@ class TestFileJpeg(PillowTestCase):
         reloaded.load()
         self.assertEqual(im.info['dpi'], reloaded.info['dpi'])
 
+    def test_load_dpi_rounding(self):
+        # Round up
+        im = Image.open('Tests/images/iptc_roundUp.jpg')
+        self.assertEqual(im.info["dpi"], (44, 44))
+
+        # Round down
+        im = Image.open('Tests/images/iptc_roundDown.jpg')
+        self.assertEqual(im.info["dpi"], (2, 2))
+
+    def test_save_dpi_rounding(self):
+        outfile = self.tempfile("temp.jpg")
+        im = Image.open('Tests/images/hopper.jpg')
+
+        im.save(outfile, dpi=(72.2, 72.2))
+        reloaded = Image.open(outfile)
+        self.assertEqual(reloaded.info["dpi"], (72, 72))
+
+        im.save(outfile, dpi=(72.8, 72.8))
+        reloaded = Image.open(outfile)
+        self.assertEqual(reloaded.info["dpi"], (73, 73))
+
     def test_dpi_tuple_from_exif(self):
         # Arrange
         # This Photoshop CC 2017 image has DPI in EXIF not metadata
diff --git a/Tests/test_file_png.py b/Tests/test_file_png.py
index 580521752..6a061fe6a 100644
--- a/Tests/test_file_png.py
+++ b/Tests/test_file_png.py
@@ -389,6 +389,24 @@ class TestFilePng(PillowTestCase):
         im = roundtrip(im, dpi=(100, 100))
         self.assertEqual(im.info["dpi"], (100, 100))
 
+    def test_load_dpi_rounding(self):
+        # Round up
+        im = Image.open(TEST_PNG_FILE)
+        self.assertEqual(im.info["dpi"], (96, 96))
+
+        # Round down
+        im = Image.open("Tests/images/icc_profile_none.png")
+        self.assertEqual(im.info["dpi"], (72, 72))
+
+    def test_save_dpi_rounding(self):
+        im = Image.open(TEST_PNG_FILE)
+
+        im = roundtrip(im, dpi=(72.2, 72.2))
+        self.assertEqual(im.info["dpi"], (72, 72))
+
+        im = roundtrip(im, dpi=(72.8, 72.8))
+        self.assertEqual(im.info["dpi"], (73, 73))
+
     def test_roundtrip_text(self):
         # Check text roundtripping
 
diff --git a/Tests/test_file_tiff.py b/Tests/test_file_tiff.py
index 34911ed50..950a449f2 100644
--- a/Tests/test_file_tiff.py
+++ b/Tests/test_file_tiff.py
@@ -126,6 +126,30 @@ class TestFileTiff(PillowTestCase):
         im._setup()
         self.assertEqual(im.info['dpi'], (71., 71.))
 
+    def test_load_dpi_rounding(self):
+        for resolutionUnit, dpi in ((None, (72, 73)),
+                                    (2, (72, 73)),
+                                    (3, (183, 185))):
+            im = Image.open(
+                "Tests/images/hopper_roundDown_"+str(resolutionUnit)+".tif")
+            self.assertEqual(im.tag_v2.get(RESOLUTION_UNIT), resolutionUnit)
+            self.assertEqual(im.info['dpi'], (dpi[0], dpi[0]))
+
+            im = Image.open("Tests/images/hopper_roundUp_"+str(resolutionUnit)+".tif")
+            self.assertEqual(im.tag_v2.get(RESOLUTION_UNIT), resolutionUnit)
+            self.assertEqual(im.info['dpi'], (dpi[1], dpi[1]))
+
+    def test_save_dpi_rounding(self):
+        outfile = self.tempfile("temp.tif")
+        im = Image.open("Tests/images/hopper.tif")
+
+        for dpi in (72.2, 72.8):
+            im.save(outfile, dpi=(dpi, dpi))
+
+            reloaded = Image.open(outfile)
+            reloaded.load()
+            self.assertEqual((round(dpi), round(dpi)), reloaded.info['dpi'])
+
     def test_save_setting_missing_resolution(self):
         b = BytesIO()
         Image.open("Tests/images/10ct_32bit_128.tiff").save(
diff --git a/Tests/test_file_wmf.py b/Tests/test_file_wmf.py
index 146888491..e3c6063f2 100644
--- a/Tests/test_file_wmf.py
+++ b/Tests/test_file_wmf.py
@@ -45,6 +45,15 @@ class TestFileWmf(PillowTestCase):
         # Restore the state before this test
         WmfImagePlugin.register_handler(None)
 
+    def test_load_dpi_rounding(self):
+        # Round up
+        im = Image.open('Tests/images/drawing.emf')
+        self.assertEqual(im.info["dpi"], 1424)
+
+        # Round down
+        im = Image.open('Tests/images/drawing_roundDown.emf')
+        self.assertEqual(im.info["dpi"], 1426)
+
     def test_save(self):
         im = hopper()
 
diff --git a/src/PIL/BmpImagePlugin.py b/src/PIL/BmpImagePlugin.py
index 9a82e526a..3ca293a94 100644
--- a/src/PIL/BmpImagePlugin.py
+++ b/src/PIL/BmpImagePlugin.py
@@ -27,7 +27,6 @@
 from . import Image, ImageFile, ImagePalette
 from ._binary import i8, i16le as i16, i32le as i32, \
                      o8, o16le as o16, o32le as o32
-import math
 
 # __version__ is deprecated and will be removed in a future version. Use
 # PIL.__version__ instead.
@@ -121,8 +120,7 @@ class BmpImageFile(ImageFile.ImageFile):
             file_info['colors'] = i32(header_data[28:32])
             file_info['palette_padding'] = 4
             self.info["dpi"] = tuple(
-                map(lambda x: int(math.ceil(x / 39.3701)),
-                    file_info['pixels_per_meter']))
+                int(x / 39.3701 + 0.5) for x in file_info['pixels_per_meter'])
             if file_info['compression'] == self.BITFIELDS:
                 if len(header_data) >= 52:
                     for idx, mask in enumerate(['r_mask',
@@ -311,7 +309,7 @@ def _save(im, fp, filename, bitmap_header=True):
     dpi = info.get("dpi", (96, 96))
 
     # 1 meter == 39.3701 inches
-    ppm = tuple(map(lambda x: int(x * 39.3701), dpi))
+    ppm = tuple(map(lambda x: int(x * 39.3701 + 0.5), dpi))
 
     stride = ((im.size[0]*bits+7)//8+3) & (~3)
     header = 40  # or 64 for OS/2 version 2
diff --git a/src/PIL/JpegImagePlugin.py b/src/PIL/JpegImagePlugin.py
index 541b84ee8..d42c5128d 100644
--- a/src/PIL/JpegImagePlugin.py
+++ b/src/PIL/JpegImagePlugin.py
@@ -160,13 +160,13 @@ def APP(self, marker):
             resolution_unit = exif[0x0128]
             x_resolution = exif[0x011A]
             try:
-                dpi = x_resolution[0] / x_resolution[1]
+                dpi = float(x_resolution[0]) / x_resolution[1]
             except TypeError:
                 dpi = x_resolution
             if resolution_unit == 3:  # cm
                 # 1 dpcm = 2.54 dpi
                 dpi *= 2.54
-            self.info["dpi"] = dpi, dpi
+            self.info["dpi"] = int(dpi + 0.5), int(dpi + 0.5)
         except (KeyError, SyntaxError, ZeroDivisionError):
             # SyntaxError for invalid/unreadable exif
             # KeyError for dpi not included
diff --git a/src/PIL/TiffImagePlugin.py b/src/PIL/TiffImagePlugin.py
index 34c6f39de..0b722b447 100644
--- a/src/PIL/TiffImagePlugin.py
+++ b/src/PIL/TiffImagePlugin.py
@@ -1260,11 +1260,11 @@ class TiffImageFile(ImageFile.ImageFile):
         if xres and yres:
             resunit = self.tag_v2.get(RESOLUTION_UNIT)
             if resunit == 2:  # dots per inch
-                self.info["dpi"] = xres, yres
+                self.info["dpi"] = int(xres + 0.5), int(yres + 0.5)
             elif resunit == 3:  # dots per centimeter. convert to dpi
-                self.info["dpi"] = xres * 2.54, yres * 2.54
+                self.info["dpi"] = int(xres * 2.54 + 0.5), int(yres * 2.54 + 0.5)
             elif resunit is None:  # used to default to 1, but now 2)
-                self.info["dpi"] = xres, yres
+                self.info["dpi"] = int(xres + 0.5), int(yres + 0.5)
                 # For backward compatibility,
                 # we also preserve the old behavior
                 self.info["resolution"] = xres, yres
@@ -1475,8 +1475,8 @@ def _save(im, fp, filename):
     dpi = im.encoderinfo.get("dpi")
     if dpi:
         ifd[RESOLUTION_UNIT] = 2
-        ifd[X_RESOLUTION] = dpi[0]
-        ifd[Y_RESOLUTION] = dpi[1]
+        ifd[X_RESOLUTION] = int(dpi[0] + 0.5)
+        ifd[Y_RESOLUTION] = int(dpi[1] + 0.5)
 
     if bits != (1,):
         ifd[BITSPERSAMPLE] = bits
diff --git a/src/PIL/WmfImagePlugin.py b/src/PIL/WmfImagePlugin.py
index 06eb851c9..413bd1847 100644
--- a/src/PIL/WmfImagePlugin.py
+++ b/src/PIL/WmfImagePlugin.py
@@ -131,8 +131,8 @@ class WmfStubImageFile(ImageFile.StubImageFile):
             size = x1 - x0, y1 - y0
 
             # calculate dots per inch from bbox and frame
-            xdpi = 2540 * (x1 - y0) // (frame[2] - frame[0])
-            ydpi = 2540 * (y1 - y0) // (frame[3] - frame[1])
+            xdpi = int(2540.0 * (x1 - y0) / (frame[2] - frame[0]) + 0.5)
+            ydpi = int(2540.0 * (y1 - y0) / (frame[3] - frame[1]) + 0.5)
 
             self.info["wmf_bbox"] = x0, y0, x1, y1